1. Will Percival The University of Portsmouth
The Theory/Observation connection lecture 4 dark energy: linking with observations
Will Percival
The University of Portsmouth

2. Lecture outline Dark Energy review Geometrical tests
cosmological constant?
quintessence?
tangled defects?
phantom dark energy?
modified gravity?
problems with the data?
Geometrical tests
SN1a
BAO

3. Cosmological constant
Originally introduced by Einstein to make the Universe static
Constant vacuum energy density, which is homogeneous and has constant density in time
Equation of state
Particle physics provides a natural candidate: zero-point vacuum fluctuations for bosonic or fermionic fields
typical scale of cosmological constant is (Mcutoff)4, where Mcutoff is UV cutoff of theory describing field
Planck mass gives planck ~ (1019GeV)4
Observations show

4. quintessence
adaption of scalar field theory developed for inflationary theories for late-time dark energy
very weak potential required, with very small effective mass
field can be frozen at early times
or it can slowly roll down the potential, with energy density tracking dominant fluid until recently (“tracker” models)
equation-of-state generally evolves, although can be constant (with special choice of potential)
In fact, any w(z)>-1 history can be obtained with right choice of potential

5. Albrecht & Weller 2002, astro-ph/0106079
quintessence
Albrecht & Weller 2002, astro-ph/

6. Parameterizations of w
If you don’t know the physics, you don’t have a well-defined set of models to test, it’s a free-for-all
can parameterise using
w(a) = w0 + w1(1-a)
Bassett et al. 2004, astro-ph/

7. Tangled defects
Network of defects formed in phase transition grows with expansion of Universe
For strings, lengths grow as a, and energy as a-2, so w=-1/3, and no acceleration (just)
For walls, area grows as a2, and energy drops as a-1, so w=-2/3, which can produce acceleration
but observations show w ~ -1

8. Phantom dark energy
motivated by early supernovae data which favored strong acceleration
w<-1
density increases as Universe expands
can lead to divergence in finite time - big rip
theoretically difficult to justify
violate weak energy condition
lead to ghosts - negative norm energy states
can be classically and quantum mechanically unstable
If observations continue to show strong acceleration at low redshifts, may need a phase shift in theory

9. modified gravity
Can separate cosmological constant from stress-energy tensor
Can then imagine moving it to the other side of the equation
Should we consider alternatives if we’re going to be modifying gravity, rather than postulating a new component of energy?

10. modified gravity Example from history: Mercury perihilion
Newton + dark planet?
No! Modified gravity (GR)
Today, we need a modified Friedmann equation

11. modified gravity
Modified gravity: replace R with f(R) in action for gravity. Gives
DGP modifed gravity (5D braneworld)
Problem: we can always explain Adark by either stress-energy component or change to gravity.
Only way of telling apart is by structure formation (see next lecture)

12. Problems with the data …
data depends on astrophysics, so subject to systematics
but, more than one test, so need a conspiracy that all the astrophysics points you to acceleration …
Still, worth reviewing all data

13. With this in mind, lets have a look at the evidence for acceleration …

14. All strong evidence is geometrical
All of the evidence depends on the expansion geometry, specifically through the Friedmann equation
equation of state of dark energy p = w(a) 

15. <w>=-1.02 ± 0.09 (stat) ± 0.054 (sys) (with BAO + Flat Universe)
SNLS Hubble diagram
First-Year SNLS Hubble Diagram
Astier et al (2006)
A&A, 447, 31
ΩM = ± (stat) ± (sys)
<w>=-1.02 ± 0.09 (stat) ± (sys) (with BAO + Flat Universe)

16. Supernovae observations
Initially assumed all SN1a have same intrinsic peak brightness
Now refined so that
Apparent magnitude of supernova
Stretch parameter s: corrects for lightcurve shape via 
Luminosity distance to supernova
Absolute magnitude of supernova (assumed constant for all SN1a)
c=B-V colour: corrects for extinction/intrinsic effects via 

17. Supernovae systematics
“Experimental Systematics”
Calibration, photometry, Malmquist-type effects
Contamination by other SNe or peculiar SNe Ia
Minimized by spectroscopic confirmation
Non-SNe systematics
Peculiar velocities; Hubble Bubble; Weak lensing
K-corrections and SN spectra
UV uncertain; “golden” redshifts; spectral evolution?
Extinction/Colour
Effective RV; Intrinsic colour versus dust
Redshift evolution in the mix of SNe
“Population drift” – environment?
Evolution in SN properties
Light-curves/Colors/Luminosities
From talk by Mark Sullivan

18. Hubble diagram by galaxy type
SNe in passive galaxies show a smaller scatter
“Intrinsic dispersion” consistent with zero
(Does intrinsic dispersion in SNe arise from dust?)
Cleaner sample: But SNe in passive galaxies are at high-z (~20%: two component model) + very few locally
Star-forming hosts
Passive hosts

19. Cosmological distribution of galaxy types

20. Future supernovae prospects
Short-term:
Current constraints on <w>: <w>=-1 to ~6-7% (stat)
(inc. flat Universe, BAO+WMAP-3)
At SNLS survey end, statistical uncertainty will be 4-5%:
500 SNLS SDSS + larger local samples
Improved external constraints (BAO, WL)
Longer term:
No evolutionary bias in cosmology detected (tests continue!)
SNe in passive galaxies: seem more powerful probes, but substantially rarer (esp. at high-z)
Colour corrections are the dominant uncertainty
Urgent need for z<0.1 samples with wide wavelength coverage
Not clear what the “next step” at high-z should be

21. Galaxy clustering

22. The power spectrum turn-over
In radiation dominated Universe, pressure support means that small perturbations cannot collapse. Jeans scale changes with time, leading to smooth turn-over of matter power spectrum.
varying the matter density
times the Hubble constant
However, it is hard to disentangle this shape change from galaxy bias and non-linear effects

23. Problem: galaxy bias
Galaxies do not form a Poisson sampling of the matter field
Peaks model: large scale offset in 2-pt clustering strength (next lecture)
Also non-linear effects in the matter
Also effects from the transition from mass to galaxies
Angulo et al., 2007, MNRAS, astro-ph/

24. Baryon Acoustic Oscillations
“Wavelength” of baryonic acoustic oscillations is determined by the comoving sound horizon at recombination
varying the
baryon fraction
At early times can ignore dark energy, so comoving sound horizon is given by
Sound speed cs
Gives the comoving sound horizon ~110h-1Mpc, and BAO wavelength 0.06hMpc-1

25. CREDIT: WMAP & SDSS websites
Comparing CMB & BAO
CMB
SDSS GALAXIES
CREDIT: WMAP & SDSS websites

26. Comparing BAO at different redshifts
SDSS main galaxies + 2dFGRS
SDSS LRGs
Tell us more about the acceleration, rather than just that we need it!
z=0.2
z=0.35
CREDIT: WMAP & SDSS websites

27. BAO as a standard ruler Gives rise to the “rings of power”
Changes in cosmological model alter measured BAO scale (∆dcomov) by:
Radial direction
(evolution of Universe)
Angular direction
(line of sight)
Gives rise to the “rings of power”
Hu & Haiman 2003, astro-ph/

28. BAO as a standard ruler
BAO position (in a redshift slice) therefore constrains some multiple of
Changes in cosmological model alter measured BAO scale (∆dcomov) by:
Radial direction
(evolution of Universe)
Angular direction
(line of sight)
If we are considering radial and angular directions using randomly placed galaxy pairs, we constrain (to 1st order)
Varying rs/DV

29. Why BAO are a good ruler Linear baryon acoustic oscillations
are ratio of linear matter power
spectrum to a smooth fit
Suppose that we measure an observed power that is related to the linear power by (halo model)
Linear bias model also predicts this form
Then observed oscillations are related to linear BAO by
For linear bias model, peculiar velocities of galaxies gives Gaussian damping with width ~10Mpc
No change in position of oscillations,
just a damping term.
To change the observed positions of BAO, we need sharp features in the observed power
Eisenstein, Seo & White 2006, astro-ph/
Percival et al. 2007, astro-ph/

30. “Renormalized Perturbation Theory (RPT)”
Going to 2nd order …
Perturbative treatment of
(CDM+baryon) fluid system
（e.g., Suto & Sasaki 1991)
New approach
Based on field-theoretical approach,
Standard PT calculation can be improved by re-summing an
infinite class of perturbative corrections at all orders.
“Renormalized Perturbation Theory (RPT)”
Crocce & Scoccimarro (2006ab,2007)
Related works: McDonald, Matarrese & Pietroni, Valageas, Matsubara (‘07)

31. Going to 2nd order …
At second order we get mode mixing, which causes shifts in the power spectrum BAO peaks
Shifts are <1%, and can be calculated
Not important for current data, but need to be included for future analyses
Crocce & Scoccimarro 2007; astro-ph/

32. BAO from all the SDSS DR5 galaxies
Compared with WMAP 3-year best fit linear CDM cosmological model.
N.B. not a fit to the data, but a prediction from WMAP.
Interesting features:
Overall P(k) shape
Observed baryon acoustic oscillations (BAO)
Percival et al., 2007, ApJ, 657, 645

33. BAO from the 2dFGRS + SDSS
BAO detected at low redshift 0<z<0.3 (effective redshift 0.2)
BAO detected at high redshift 0.15<z<0.5 (effective redshift 0.35)
BAO from combined sample (detected over the whole redshift range 0<z<0.5)
Percival et al., 2007, MNRAS, astro-ph/

34. BAO distance scale constraints
Constraint including observed peak distance constrain from CMB rs/dA(cmb)=0.0104
CDM
OCDM
SCDM
Constraint fitting rs/DV(z)
Constraint from
DV(0.35)/DV(0.2)

35. Future BAO prospects
Short-term:
SDSS-II improves low redshift measurements by factor ~2
galaxy redshifts to z~0.5
Wiggle-Z survey detects BAO at higher redshift
galaxy redshifts to z~1
weak constraints
Longer term:
Photometric surveys (e.g PanSTARRS, DES) find ~2--3% distance constraints out to z~1
Future spectroscopic surveys (e.g. HetDex, BOSS, WFMOS, Space) push to 1% distance constraints over a wide range of redshift (0.5<z<3)
With 1% constraints need to include 2nd order effects in analysis of BAO positions

36. Further reading Supernovae Astier et al. (2005), astro-ph/0510447 BAO
Blake & Glazebrook (2003), astro-ph/
Seo & Eisenstein (2003), ApJ, 598, 720
Hu & Haiman (2003), astro-ph/